Finite Group Databasebeta

← D3×#66047 #14484725

Subgroups — D3×#66047 #14484725

Order 1920.

2480 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756472C211yesmaximal, characteristic, complemented
2C5×D3×#127C211yesmaximal, characteristic
3C3×#66047C211yesmaximal, characteristic, complemented
4#11754889C214yesmaximal, complemented
5#11754888C214yesmaximal, complemented
6#11754887C214yesmaximal, complemented
7D3×#4082C214yesmaximal, complemented
8D3×#4081C214yesmaximal, complemented
9D3×D4×Dic5C214yesmaximal, complemented
10#11752651C212yesmaximal, complemented
11C4×D3×Dic10C212yesmaximal, complemented
12C2×#66047—31nomaximal, Hall
13C2×C5×D3×D4C2214yes—
14C2×C5×D3×D4C2212yes—
15C22×D3×Dic5C2214yes—
16C2×D3×Dic10C2212yes—
17C3×C5×#127C2211yescharacteristic
18#91825C2214yescomplemented
19#91824C2214yescomplemented
20D4×Dic15C2214yescomplemented
21C4×Dic30C2212yescomplemented
22C5×#940C2214yes—
23C5×#940C2212yes—
24C5×#874C2211yescharacteristic
25C42×C5×D3C2211yescharacteristic
26C3×#4082C2214yescomplemented
27C3×#4081C2214yescomplemented
28C3×D4×Dic5C2214yescomplemented
29C3×C4×Dic10C2212yescomplemented
30#67⋊Dic5C2218yescomplemented
31#91555C2218yescomplemented
32D3×C22⋊Dic5C2218yes—
33D3×C22⋊Dic5C2214yes—
34Dic5×#67C2218yescomplemented
35#91543C2214yescomplemented
36#91539C2214yescomplemented
37#91525C2218yescomplemented
38#91525C2218yescomplemented
39C4×#1204C2214yescomplemented
40#91435C2214yescomplemented
41D3×C4⋊Dic5C2212yes—
42#91423C2218yescomplemented
43Dic5×D12C2214yescomplemented
44D3×#683C2214yes—
45C4×D3×Dic5C2214yes—
46#91373C2214yescomplemented
47#91370C2214yescomplemented
48#91340C2212yescomplemented
49Dic3×Dic10C2212yescomplemented
50#91324C2214yescomplemented
51D3×#559—51nomaximal, Hall
52C2×C5×#127—31no—
53C2×#4082—34no—
54C2×#4081—34no—
55C2×D4×Dic5—34no—
56#66047—34no—
57#66047—34no—
58#66047—34no—
59#66047—32no—
60#66047—31no—
61#66047D311yescharacteristic, direct product factor
62C2×C4×Dic10—32no—
63C23×C5×D3C2314yes—
64C2×C3×C5×D4C2314yes—
65C2×C3×C5×D4C2312yes—
66C22×Dic15C2314yes—
67C2×Dic30C2312yes—
68C2×C5×#67C2318yes—
69C2×C5×#67C2314yes—
70C5×D3×D4—216no—
71C5×D3×D4—44no—
72C2×C5×D12C2314yes—
73C2×C5×D12C2312yes—
74C2×C4×C5×D3C2311yescharacteristic
75C2×C4×C5×D3C2312yes—
76C22×C3×Dic5C2314yes—
77C2×C3×Dic10C2312yes—
78C2×#1204C2314yes—
79C2×D3×Dic5—48no—
80C2×D3×Dic5C2314yes—
81C2×D3×Dic5C2314yes—
82C2×D3×Dic5C2318yes—
83D3×Dic10—28no—
84C3×C42×C5C2311yescharacteristic
85#6719C2314yes—
86#6719C2318yes—
87C4⋊Dic15C2312yes—
88#6712C2314yes—
89C4×Dic15C2314yes—
90C4×C5×Dic3C2312yes—
91C4×C5×Dic3C2311yescharacteristic
92C3×C22⋊Dic5C2318yes—
93C3×C22⋊Dic5C2314yes—
94C3×C4⋊Dic5C2312yes—
95C3×#683C2314yes—
96C3×C4×Dic5C2314yes—
97Dic3⋊Dic5C2314yes—
98#6669C2314yes—
99#6668C2314yes—
100(C2×D3)⋊Dic5C2318yes—
101(C2×D3)⋊Dic5C2318yes—
102(C2×D3)⋊Dic5C2318yes—
103Dic3×Dic5C2314yes—
104Dic3×Dic5C2314yes—
105C3×#559—51no—
106D3×#127D511yescharacteristic
107#5713—51no—
108#5681—54no—
109D3×#124—54no—
110#5664—54no—
111D3×#123—54no—
112#5585—52no—
113C4×D3×Q8—52no—
114#5559—54no—
115C4×D3×D4—54no—
116C22×C5×D4—34no—
117C22×C5×D4—32no—
118C23×Dic5—34no—
119C22×Dic10—32no—
120C5×#127—32no—
121C5×#127—34no—
122C5×#127—31no—
123C5×#127C2×D311yescharacteristic
124C2×C42×C5—31no—
125C2×C22⋊Dic5—38no—
126C2×C22⋊Dic5—34no—
127#4082—34no—
128#4082—34no—
129#4082—38no—
130#4082—38no—
131#4082—34no—
132#4082C2×D314yescomplemented
133#4081—34no—
134#4081—34no—
135#4081—34no—
136#4081—38no—
137#4081—38no—
138#4081C2×D314yescomplemented
139D4×Dic5—34no—
140D4×Dic5—38no—
141D4×Dic5—38no—
142D4×Dic5—34no—
143D4×Dic5—34no—
144D4×Dic5C2×D314yescomplemented
145C2×C4⋊Dic5—32no—
146C2×#683—34no—
147C2×C4×Dic5—34no—
148C4×Dic10—32no—
149C4×Dic10—32no—
150C4×Dic10—32no—
151C4×Dic10—34no—
152C4×Dic10—34no—
153C4×Dic10C2×D312yescomplemented
154C2×#559—151noSylow
155C23×C3×C5C2414yes—
156C22×C5×D3—216no—
157C22×C5×D3—28no—
158C22×C5×D3C2414yes—
159C22×C5×D3C2411yescharacteristic
160C3×C5×D4—28no—
161C3×C5×D4—42no—
162C2×C3×C4×C5C2411yescharacteristic
163C2×C3×C4×C5C2412yes—
164C2×Dic15—44no—
165C2×Dic15C2414yes—
166C2×Dic15C2414yes—
167Dic30—24no—
168C5×#67—216no—
169C5×#67—44no—
170C2×C5×Dic3C2411yescharacteristic
171C2×C5×Dic3C2412yes—
172C5×D12—28no—
173C5×D12—42no—
174C4×C5×D3—22no—
175C4×C5×D3#4118yes—
176C2×C3×Dic5—44no—
177C2×C3×Dic5C2414yes—
178C2×C3×Dic5C2414yes—
179C3×Dic10—24no—
180#1204—28no—
181D3×Dic5—28no—
182D3×Dic5—28no—
183D3×Dic5—48no—
184C2×D3×Q8—52no—
185C2×D3×D4C2×D514yes—
186C2×D3×D4C2×D512yes—
187C22×C4×D3—54no—
188C3×#127C2×D511yescharacteristic
189C3×#124—54no—
190C3×#123—54no—
191C3×C4×Q8—52no—
192C3×C4×D4—54no—
193#947—54no—
194Q8×Dic3—52no—
195#940C2×D512yes—
196#940C2×D514yes—
197#936—54no—
198#935—54no—
199D4×Dic3—54no—
200#929—54no—
201C4×#67—58no—
202#894—58no—
203#893—54no—
204D3×C4⋊C4—54no—
205D3×C4⋊C4—52no—
206#887—54no—
207#887—52no—
208#886—54no—
209#885—58no—
210#885—58no—
211#883—58no—
212#67⋊C4—58no—
213D3×C22⋊C4—54no—
214D3×C22⋊C4—58no—
215#875—54no—
216#874C2×D511yescharacteristic
217C4×D12—54no—
218C42×D3—54no—
219C42×D3C2×D511yescharacteristic
220C4×Dic6—52no—
221C4×Dic6—54no—
222C24×C5—34no—
223C2×C5×D4—38no—
224C2×C5×D4—34no—
225C2×C5×D4—34no—
226C2×C5×D4—32no—
227C2×C5×D4—616no—
228C2×C5×D4—124no—
229C2×C5×D4C22×D314yes—
230C2×C5×D4C22×D312yes—
231C22×C4×C5—32no—
232C22×C4×C5—31no—
233C22×Dic5—34no—
234C22×Dic5—34no—
235C22×Dic5—34no—
236C22×Dic5—38no—
237C22×Dic5—128no—
238C22×Dic5C22×D314yes—
239C2×Dic10—32no—
240C2×Dic10—34no—
241C2×Dic10—68no—
242C2×Dic10C22×D312yes—
243C42×C5—31no—
244C42×C5—32no—
245C42×C5C22×D311yescharacteristic
246C22⋊Dic5—38no—
247C22⋊Dic5—34no—
248C22⋊Dic5—38no—
249C22⋊Dic5—38no—
250C22⋊Dic5—38no—
251C22⋊Dic5C22×D318yes—
252C22⋊Dic5C22×D314yes—
253C4⋊Dic5—32no—
254C4⋊Dic5—34no—
255C4⋊Dic5C22×D312yes—
256#683—34no—
257#683—34no—
258#683—34no—
259#683C22×D314yes—
260C4×Dic5—34no—
261C4×Dic5—34no—
262C4×Dic5—34no—
263C4×Dic5C22×D314yes—
264#559—51no—
265#559—154no—
266#559—152no—
267#559—154no—
268#559—154no—
269#559—151no—
270C2×#127—31no—
271C2×#124—154no—
272C2×#123—154no—
273C2×C4×Q8—152no—
274C2×C4×D4—154no—
275C22×C3×C5—28no—
276C22×C3×C5—24no—
277C22×C3×C5C2511yescharacteristic
278C2×C5×D3—28no—
279C2×C5×D3—24no—
280C2×C5×D3—416no—
281C2×C5×D3C2×#4114yes—
282C2×C5×D3H(5,𝔽2)12yes—
283C3×C4×C5—21no—
284C3×C4×C5C2×#4114yes—
285Dic15—24no—
286Dic15—24no—
287C3×Dic5—24no—
288C3×Dic5—24no—
289C5×Dic3—21no—
290C5×Dic3C2×#4114yes—
291C23×D3C22×D514yes—
292C2×C3×Q8—52no—
293C2×C3×D4C22×D514yes—
294C2×C3×D4C22×D512yes—
295C22×C3×C4—54no—
296C2×#67C22×D518yes—
297C2×#67C22×D514yes—
298C22×Dic3—54no—
299D3×Q8—108no—
300D3×D4—216no—
301D3×D4—44no—
302C2×D12C22×D514yes—
303C2×D12C22×D512yes—
304C2×C4×D3—54no—
305C2×C4×D3—54no—
306C2×C4×D3—58no—
307C2×C4×D3—208no—
308C2×C4×D3C22×D511yescharacteristic
309C2×C4×D3C22×D512yes—
310C2×Dic6—52no—
311C2×Dic6—54no—
312C3×C4⋊C4—54no—
313C3×C4⋊C4—52no—
314C3×C22⋊C4—58no—
315C3×C22⋊C4—54no—
316C3×C42—54no—
317C3×C42C22×D511yescharacteristic
318#217—58no—
319#217—54no—
320(C2×D3)⋊C4—58no—
321(C2×D3)⋊C4—58no—
322(C2×D3)⋊C4—58no—
323C4⋊Dic3—52no—
324C4⋊Dic3—54no—
325Dic3⋊C4—54no—
326Dic3⋊C4—54no—
327Dic3⋊C4—54no—
328C4×Dic3—54no—
329C4×Dic3—54no—
330C4×Dic3—54no—
331C4×Dic3C22×D512yes—
332C4×Dic3C22×D511yescharacteristic
333C23×C5—31no—
334C23×C5—34no—
335C23×C5—68no—
336C23×C5—616no—
337C23×C5C23×D314yes—
338C5×D4—28no—
339C5×D4—42no—
340C5×D4—616no—
341C5×D4—68no—
342C5×D4—122no—
343C5×D4—124no—
344C2×C4×C5—32no—
345C2×C4×C5—38no—
346C2×C4×C5—31no—
347C2×C4×C5—62no—
348C2×C4×C5C23×D311yescharacteristic
349C2×C4×C5C23×D312yes—
350C2×Dic5—34no—
351C2×Dic5—34no—
352C2×Dic5—44no—
353C2×Dic5—68no—
354C2×Dic5—68no—
355C2×Dic5—128no—
356C2×Dic5—124no—
357C2×Dic5C23×D314yes—
358C2×Dic5C23×D314yes—
359Dic10—24no—
360Dic10—68no—
361Dic10—64no—
362C22×Q8—152no—
363C22×D4—34no—
364C22×D4—32no—
365C23×C4—154no—
366#127—32no—
367#127—34no—
368#127—31no—
369#127D3×D511yescharacteristic
370#124—54no—
371#124—154no—
372#124—158no—
373#124—158no—
374#124—154no—
375#124—154no—
376#123—54no—
377#123—158no—
378#123—154no—
379#123—158no—
380#123—154no—
381#123—154no—
382C4×Q8—52no—
383C4×Q8—154no—
384C4×Q8—152no—
385C4×Q8—154no—
386C4×Q8—152no—
387C4×Q8—152no—
388C4×D4—54no—
389C4×D4—154no—
390C4×D4—158no—
391C4×D4—154no—
392C4×D4—158no—
393C4×D4—154no—
394C2×C4⋊C4—152no—
395C2×C4⋊C4—154no—
396C2×C22⋊C4—158no—
397C2×C22⋊C4—154no—
398C2×C42—31no—
399C2×C42—154no—
400C2×C3×C5—44no—
401C2×C3×C5C22×#4112yes—
402C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
403C5×D3—44no—
404C5×D3#55914yescomplemented
405C23×C3C23×D514yes—
406C22×D3—216no—
407C22×D3—28no—
408C22×D3C23×D514yes—
409C22×D3C23×D511yescharacteristic
410C3×Q8—104no—
411C3×D4—28no—
412C3×D4—42no—
413C2×C3×C4—54no—
414C2×C3×C4—54no—
415C2×C3×C4—204no—
416C2×C3×C4C23×D511yescharacteristic
417C2×C3×C4C23×D512yes—
418#67—216no—
419#67—44no—
420C2×Dic3—54no—
421C2×Dic3—54no—
422C2×Dic3—204no—
423C2×Dic3C23×D511yescharacteristic
424C2×Dic3C23×D512yes—
425D12—28no—
426D12—42no—
427C4×D3—22no—
428C4×D3—108no—
429C4×D3—108no—
430C4×D3—208no—
431C4×D3#71118yes—
432Dic6—104no—
433Dic6—108no—
434C22×C5—28no—
435C22×C5—24no—
436C22×C5—34no—
437C22×C5—32no—
438C22×C5—68no—
439C22×C5—64no—
440C22×C5—1216no—
441C22×C5C24×D311yescharacteristic
442C4×C5—21no—
443C4×C5—34no—
444C4×C5—61no—
445C4×C5D3×#4114yes—
446Dic5—24no—
447Dic5—24no—
448Dic5—64no—
449Dic5—64no—
450C24—34no—
451C2×Q8—52no—
452C2×Q8—154no—
453C2×Q8—152no—
454C2×Q8—308no—
455C2×D4—38no—
456C2×D4—34no—
457C2×D4—34no—
458C2×D4—32no—
459C2×D4—616no—
460C2×D4—124no—
461C2×D4C2×D3×D514yes—
462C2×D4C2×D3×D512yes—
463C22×C4—32no—
464C22×C4—31no—
465C22×C4—54no—
466C22×C4—154no—
467C22×C4—154no—
468C22×C4—158no—
469C22×C4—154no—
470C22×C4—608no—
471C4⋊C4—52no—
472C4⋊C4—54no—
473C4⋊C4—154no—
474C4⋊C4—154no—
475C4⋊C4—154no—
476C4⋊C4—152no—
477C4⋊C4—154no—
478C22⋊C4—58no—
479C22⋊C4—54no—
480C22⋊C4—158no—
481C22⋊C4—158no—
482C22⋊C4—158no—
483C22⋊C4—158no—
484C22⋊C4—154no—
485C42—31no—
486C42—32no—
487C42—54no—
488C42—154no—
489C42—154no—
490C42—154no—
491C42C2×D3×D511yescharacteristic
492C3×C5C2×#55911yescharacteristic, complemented, Hall
493C22×C3—28no—
494C22×C3—24no—
495C22×C3C24×D511yescharacteristic
496C2×D3—28no—
497C2×D3—24no—
498C2×D3—416no—
499C2×D3C2×#71114yes—
500C2×D3#414412yes—
501C3×C4—21no—
502C3×C4—104no—
503C3×C4—104no—
504C3×C4C2×#71114yes—
505Dic3—21no—
506Dic3—104no—
507Dic3—104no—
508Dic3C2×#71114yes—
509C2×C5—34no—
510C2×C5—44no—
511C2×C5—124no—
512C2×C5C2×D3×#4112yes—
513C2×C5D3×H(5,𝔽2)11yescharacteristic
514C23—31no—
515C23—34no—
516C23—68no—
517C23—616no—
518C23C22×D3×D514yes—
519Q8—104no—
520Q8—308no—
521Q8—304no—
522D4—28no—
523D4—42no—
524D4—616no—
525D4—68no—
526D4—122no—
527D4—124no—
528C2×C4—32no—
529C2×C4—38no—
530C2×C4—31no—
531C2×C4—54no—
532C2×C4—54no—
533C2×C4—62no—
534C2×C4—154no—
535C2×C4—154no—
536C2×C4—204no—
537C2×C4—308no—
538C2×C4—308no—
539C2×C4—608no—
540C2×C4—604no—
541C2×C4C22×D3×D511yescharacteristic
542C2×C4C22×D3×D512yes—
543C2×C3—44no—
544C2×C3C22×#71112yes—
545C2×C3C2×#414411yescharacteristic
546D3—44no—
547D3#6604714yesdirect product factor
548C5D3×#55911yescharacteristic, complemented, Sylow
549C22—28no—
550C22—24no—
551C22—34no—
552C22—32no—
553C22—68no—
554C22—64no—
555C22—1216no—
556C22C23×D3×D511yescharacteristic
557C4—21no—
558C4—34no—
559C4—61no—
560C4—104no—
561C4—104no—
562C4—304no—
563C4—304no—
564C4D3×#71114yes—
565C3C2×#6604711yescharacteristic, complemented, Sylow
566C2—34no—
567C2—44no—
568C2—124no—
569C2C2×D3×#71112yes—
570C2D3×#414411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C5×#127C22
prime radicalC5×D3×#127C2
hypercenter#127D3×D5
hypocenterC3×C5C2×#559
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #127

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #11756472C2semidirect
3. C3×#66047C2semidirect
4. #11754889C2semidirect
5. #11754888C2semidirect
6. #11754887C2semidirect
7. D3×#4082C2semidirect
8. D3×#4081C2semidirect
9. D3×D4×Dic5C2semidirect
10. #11752651C2semidirect
11. C4×D3×Dic10C2semidirect
18. #91825C22semidirect
19. #91824C22semidirect
20. D4×Dic15C22semidirect
21. C4×Dic30C22semidirect
26. C3×#4082C22semidirect
27. C3×#4081C22semidirect
28. C3×D4×Dic5C22semidirect
29. C3×C4×Dic10C22semidirect
30. #67⋊Dic5C22semidirect
31. #91555C22semidirect
34. Dic5×#67C22semidirect
35. #91543C22semidirect
36. #91539C22semidirect
37. #91525C22semidirect
38. #91525C22semidirect
39. C4×#1204C22semidirect
40. #91435C22semidirect
42. #91423C22semidirect
43. Dic5×D12C22semidirect
46. #91373C22semidirect
47. #91370C22semidirect
48. #91340C22semidirect
49. Dic3×Dic10C22semidirect
50. #91324C22semidirect
61. #66047D3direct (N × H)
132. #4082C2×D3semidirect
138. #4081C2×D3semidirect
144. D4×Dic5C2×D3semidirect
153. C4×Dic10C2×D3semidirect
404. C5×D3#559semidirect
492. C3×C5C2×#559semidirect
547. D3#66047direct (N × H)
548. C5D3×#559semidirect
565. C3C2×#66047semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117564722
C5×D3×#1272
C3×#660472
#117548892
#117548882
#117548872
D3×#40822
D3×#40812
D3×D4×Dic52
#117526512
C4×D3×Dic102
C2×#660473
D3×#5595